Nick Clegg will open a new front in his criticism of David Cameron on Monday by mocking his "1950s view" of the traditional British family, in which the "suit-wearing dad" is the breadwinner and the "aproned" mother the homemaker. The deputy prime minister, in a speech to the Demos thinktank, will also take issue with Cameron's defining idea of a "big society" based upon the institutions of marriage, the family, the church and voluntary organisations.

After a week dominated by his rift with Cameron over Europe, Clegg's latest attempt to assert his political philosophy and set out his differences with the prime minister will infuriate Tory MPs – many of whom privately doubt whether the Tory-Lib Dem coalition can last a full five-year term.

The intervention comes after Cameron, in a speech on Saturday, stressed the importance of religious faith as a force for good in society, saying it provided people with "a moral code" upon which to run their lives.

Stressing the Lib Dems' "progressive" credentials, Clegg will make clear that his party would never support Tory plans for tax breaks for married couples – an idea he said was the product of a party that failed to notice social changes until well after they had happened. "The institutions of our society are constantly evolving," Clegg will say. "Just look at the way the roles of men and women, and attitudes to marriage and divorce, have changed over the last century. We should not take a particular version of the family institution, such as the 1950s model of the suit-wearing, bread-winning dad and aproned, homemaking mother, and try to preserve it in aspic."

Instead, he will back his own vision of an "open society" where power is vested in people rather than state or social institutions, and married people are not placed on a moral pedestal. He will add: "We can all agree that strong relationships between parents are important, but not agree that the state should use the tax system to encourage a particular family form. Open society liberals are progressive: we believe that the future can and ought to be better than the past. Conservatives, by definition, tend to defend the status quo, embracing change reluctantly and often after the event."

Clegg's aides denied that the speech amounted to an attack on the values espoused by Cameron, or his "big society" plan. They said the event had been planned for months and was an opportunity for the deputy prime minister to lay out his "core political philosophy". They also stressed that the Lib Dems had made clear their different views on tax breaks for married couples during coalition negotiations. But Clegg's decision to press ahead with his speech before tensions over Europe had abated surprised some in the party.

One Lib Dem minister said it showed Cameron's decision to veto a new European treaty had undermined the trust between the two men. Clegg, who described Tory Eurosceptics as "xenophobic" in a Guardian interview, will contrast his party's "internationalist" outlook with the "narrow nationalism" of others.

A growing number of Tory MPs now say privately that it will not be in the national interest for the coalition to continue if the differences between Lib Dems and Tories over Europe cannot be resolved. Tory Eurosceptics were delighted by Cameron's decision to veto a new EU treaty, forcing the other 26 member states to press ahead with their own intergovernmental deal. But Clegg, who was furious at the outcome, is now trying to take a lead in bringing the UK back into discussions to ensure it is not left isolated.

However, the Tory right say they will not allow Cameron to backtrack on the veto. Bill Cash, a veteran Eurosceptic, said: "Once you have crossed the Rubicon, you cannot go back across it again." Another leading Eurosceptic, Bernard Jenkin, suggested that if Cameron gave way to Clegg's demands and allowed eurozone and other EU states to use EU institutions to administer their new fiscal union pact, then Tory MPs would renew their calls for a referendum.

"If we were to agree that the treaty of 17-plus should be able to use the EU institutions, how would ministers explain the difference between that arrangement and the treaty at 27, which they vetoed, and which would have triggered demands for a referendum?"

Other Tory MPs privately said that Cameron, having won a hero's reception from his MPs last week, should increase his efforts to appeal to the Eurosceptics in his party in order to force the Lib Dems out of the coalition.

• Tory MP Aidan Burley was sacked by David Cameron as a parliamentary aide last night after attending a stag party where guests dressed as Nazis. A party spokesman said: "Aidan Burley has behaved in a manner which is offensive and foolish. That is why he is being removed from his post."